Implement the abstract ring of multivariate polynomials, with several bases (Schur schubert, ...)

[nthiery]

We build an implantation of polynomials as formal sum of exponents. This allows to work on any number of variables with some easy morphism. We use some actions of Weyl group on the exponents to create operators (especially divided difference operators).

These operators allow us to build different bases that comes from geometry and have nice combinatorial description.

CC: @sagetrac-sage-combinat @VivianePons @tscrim @opechenik

Component: combinatorics

Keywords: multivariate polynomials, schubert polynomials, non symmetric polynomials, days54, fpsac2019

Author: Viviane Pons

Branch/Commit: public/combinat/polynomial_bases-6629 @ d6e1201

Issue created by migration from https://trac.sagemath.org/ticket/6629

[VivianePons]

Author: Viviane Pons

[VivianePons]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
-See: http://wiki.sagemath.org/combinat/MultivariatePolynomials
+We build an implantation of polynomials as formal sum of exponents. This allows to work on any number of variables with some easy morphism. We use some actions of Weyl group on the exponents to create operators (especially divided difference operators). 
+
+These operators allow us to build different bases that comes from geometry and have nice combinatorial description.

[VivianePons]

comment:2

the patch apply on 5.6 and is mostly working. It is not yet ready for review though, it needs more tests and docs and possibly a few fixes.

[jeffpferreira]

comment:3

What is the status of this ticket? Is it still in development?

[VivianePons]

comment:4

Yes, sorry for taking such a long time but this is a big implementation and I work on it only when I have time (which is not so often).
My plan is to finish a first version of it on the upcoming Sage days in Paris and find someone to work on the review.
In the meantime, the patch is working already and some people use it.

[VivianePons]

comment:5

Attachment: trac_6629-multivariate-polynomials-on-several-bases-vp.patch.gz

Just attached the last version of the patch to apply on Sage 5.9